Title :
EXIT Functions for LT and Raptor Codes, and Asymptotic Ranks of Random Matrices
Author :
Pakzad, P. ; Shokrollahi, A.
Author_Institution :
Digital Fountain, Inc., Fremont, CA
Abstract :
In this paper we propose a notion of EXIT functions for LT-codes and Raptor codes, and discuss some of their useful properties that can be used to design good codes. We will further use these results to derive interesting conclusions on ranks of random matrices. New expressions for the asymptotic ranks of certain classes of random binary matrices are derived and the results are compared to previously known bounds and results.
Keywords :
binary codes; matrix algebra; EXIT functions; Raptor codes; asymptotic ranks; random binary matrices; Algorithm design and analysis; Belief propagation; Error correction codes; Iterative algorithms; Iterative decoding; Parity check codes; Performance analysis; Physics; Sparse matrices; Turbo codes;
Conference_Titel :
Information Theory, 2007. ISIT 2007. IEEE International Symposium on
Conference_Location :
Nice
Print_ISBN :
978-1-4244-1397-3
DOI :
10.1109/ISIT.2007.4557260
